LMFDB - Embedded newform 800.2.bq.c.223.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [800,2,Mod(63,800)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(800, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 19]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("800.63");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 800 = 2^{5} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	800.bq (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.38803216170$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			223.5
Character	$\chi$	$=$	800.223
Dual form			800.2.bq.c.287.5

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.366689 + 0.719668i) q^{3} +(-0.581776 - 2.15906i) q^{5} +(1.82087 + 1.82087i) q^{7} +(1.37989 - 1.89926i) q^{9} +(-2.56052 - 3.52425i) q^{11} +(-0.435508 - 2.74969i) q^{13} +(1.34048 - 1.21039i) q^{15} +(-3.87720 - 1.97553i) q^{17} +(-0.914631 - 2.81494i) q^{19} +(-0.642727 + 1.97811i) q^{21} +(-0.658396 + 4.15695i) q^{23} +(-4.32307 + 2.51218i) q^{25} +(4.26611 + 0.675685i) q^{27} +(1.54965 + 0.503512i) q^{29} +(10.0043 - 3.25059i) q^{31} +(1.59738 - 3.13503i) q^{33} +(2.87202 - 4.99069i) q^{35} +(3.29071 - 0.521197i) q^{37} +(1.81917 - 1.32170i) q^{39} +(-8.06571 - 5.86008i) q^{41} +(2.01659 - 2.01659i) q^{43} +(-4.90341 - 1.87433i) q^{45} +(-0.681030 + 0.347002i) q^{47} -0.368901i q^{49} -3.51471i q^{51} +(-4.65994 + 2.37436i) q^{53} +(-6.11942 + 7.57863i) q^{55} +(1.69044 - 1.69044i) q^{57} +(-0.111573 - 0.0810625i) q^{59} +(9.77366 - 7.10098i) q^{61} +(5.97090 - 0.945698i) q^{63} +(-5.68337 + 2.53999i) q^{65} +(2.64671 - 5.19446i) q^{67} +(-3.23305 + 1.05048i) q^{69} +(-0.559408 - 0.181763i) q^{71} +(15.0889 + 2.38985i) q^{73} +(-3.39316 - 2.18999i) q^{75} +(1.75483 - 11.0795i) q^{77} +(-3.31359 + 10.1982i) q^{79} +(-1.09829 - 3.38020i) q^{81} +(0.0483434 + 0.0246322i) q^{83} +(-2.00963 + 9.52042i) q^{85} +(0.205879 + 1.29987i) q^{87} +(8.88915 + 12.2349i) q^{89} +(4.21381 - 5.79981i) q^{91} +(6.00781 + 6.00781i) q^{93} +(-5.54552 + 3.61241i) q^{95} +(-5.19630 - 10.1983i) q^{97} -10.2267 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 2 q^{5} - 4 q^{7} + 4 q^{13} - 22 q^{15} + 8 q^{17} + 18 q^{19} - 16 q^{21} - 8 q^{23} + 40 q^{25} - 18 q^{27} + 20 q^{31} + 44 q^{33} - 38 q^{35} - 10 q^{37} + 36 q^{39} - 16 q^{41} - 32 q^{43}+ \cdots - 132 q^{99}+O(q^{100}) $ 64 * q + 2 * q^5 - 4 * q^7 + 4 * q^13 - 22 * q^15 + 8 * q^17 + 18 * q^19 - 16 * q^21 - 8 * q^23 + 40 * q^25 - 18 * q^27 + 20 * q^31 + 44 * q^33 - 38 * q^35 - 10 * q^37 + 36 * q^39 - 16 * q^41 - 32 * q^43 + 14 * q^45 - 8 * q^47 - 22 * q^53 + 24 * q^55 - 8 * q^57 + 4 * q^59 - 36 * q^61 - 18 * q^63 - 24 * q^65 + 26 * q^67 + 60 * q^69 - 70 * q^71 - 12 * q^73 - 66 * q^75 + 48 * q^77 - 16 * q^79 - 24 * q^81 + 52 * q^83 - 46 * q^85 + 144 * q^87 - 60 * q^89 + 30 * q^91 + 20 * q^93 + 8 * q^95 - 56 * q^97 - 132 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/800\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$577$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{20}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.366689	+	0.719668i	0.211708	+	0.415501i	0.972302	−	0.233727i	$-0.0750922\pi$
$3$	0.366689	+	0.719668i	0.211708	+	0.415501i	−0.760594	+	0.649228i	$0.775092\pi$
$4$		0			0
$5$	−0.581776	−	2.15906i	−0.260178	−	0.965561i
$5$	−0.581776	−	2.15906i	−0.260178	−	0.965561i
$6$		0			0
$7$	1.82087	+	1.82087i	0.688222	+	0.688222i	0.961839	−	0.273617i	$-0.0882199\pi$
$7$	1.82087	+	1.82087i	0.688222	+	0.688222i	−0.273617	+	0.961839i	$0.588220\pi$
$8$		0			0
$9$	1.37989	−	1.89926i	0.459965	−	0.633087i
$10$		0			0
$11$	−2.56052	−	3.52425i	−0.772025	−	1.06260i	−0.996118	−	0.0880330i	$-0.971942\pi$
$11$	−2.56052	−	3.52425i	−0.772025	−	1.06260i	0.224093	−	0.974568i	$-0.428058\pi$
$12$		0			0
$13$	−0.435508	−	2.74969i	−0.120788	−	0.762626i	−0.971508	−	0.237007i	$-0.923834\pi$
$13$	−0.435508	−	2.74969i	−0.120788	−	0.762626i	0.850720	−	0.525619i	$-0.176166\pi$
$14$		0			0
$15$	1.34048	−	1.21039i	0.346109	−	0.312521i
$16$		0			0
$17$	−3.87720	−	1.97553i	−0.940359	−	0.479137i	−0.0845448	−	0.996420i	$-0.526944\pi$
$17$	−3.87720	−	1.97553i	−0.940359	−	0.479137i	−0.855815	+	0.517283i	$0.826944\pi$
$18$		0			0
$19$	−0.914631	−	2.81494i	−0.209831	−	0.645792i	−0.999480	−	0.0322345i	$-0.989738\pi$
$19$	−0.914631	−	2.81494i	−0.209831	−	0.645792i	0.789650	−	0.613558i	$-0.210262\pi$
$20$		0			0
$21$	−0.642727	+	1.97811i	−0.140255	+	0.431659i
$22$		0			0
$23$	−0.658396	+	4.15695i	−0.137285	+	0.866783i	0.818882	+	0.573962i	$0.194594\pi$
$23$	−0.658396	+	4.15695i	−0.137285	+	0.866783i	−0.956167	+	0.292821i	$0.905406\pi$
$24$		0			0
$25$	−4.32307	+	2.51218i	−0.864615	+	0.502435i
$26$		0			0
$27$	4.26611	+	0.675685i	0.821013	+	0.130036i
$28$		0			0
$29$	1.54965	+	0.503512i	0.287763	+	0.0934999i	0.449342	−	0.893360i	$-0.351659\pi$
$29$	1.54965	+	0.503512i	0.287763	+	0.0934999i	−0.161579	+	0.986860i	$0.551659\pi$
$30$		0			0
$31$	10.0043	−	3.25059i	1.79682	−	0.583823i	0.797026	−	0.603945i	$-0.206405\pi$
$31$	10.0043	−	3.25059i	1.79682	−	0.583823i	0.999798	+	0.0201213i	$0.00640523\pi$
$32$		0			0
$33$	1.59738	−	3.13503i	0.278067	−	0.545738i
$34$		0			0
$35$	2.87202	−	4.99069i	0.485460	−	0.843581i
$36$		0			0
$37$	3.29071	−	0.521197i	0.540990	−	0.0856843i	0.120041	−	0.992769i	$-0.461697\pi$
$37$	3.29071	−	0.521197i	0.540990	−	0.0856843i	0.420948	+	0.907085i	$0.361697\pi$
$38$		0			0
$39$	1.81917	−	1.32170i	0.291300	−	0.211642i
$40$		0			0
$41$	−8.06571	−	5.86008i	−1.25965	−	0.915191i	−0.260912	−	0.965363i	$-0.584023\pi$
$41$	−8.06571	−	5.86008i	−1.25965	−	0.915191i	−0.998741	+	0.0501717i	$0.984023\pi$
$42$		0			0
$43$	2.01659	−	2.01659i	0.307527	−	0.307527i	−0.536423	−	0.843950i	$-0.680225\pi$
$43$	2.01659	−	2.01659i	0.307527	−	0.307527i	0.843950	+	0.536423i	$0.180225\pi$
$44$		0			0
$45$	−4.90341	−	1.87433i	−0.730957	−	0.279409i
$46$		0			0
$47$	−0.681030	+	0.347002i	−0.0993384	+	0.0506154i	−0.502954	−	0.864313i	$-0.667753\pi$
$47$	−0.681030	+	0.347002i	−0.0993384	+	0.0506154i	0.403615	+	0.914929i	$0.367753\pi$
$48$		0			0
$49$		−	0.368901i		−	0.0527001i
$50$		0			0
$51$		−	3.51471i		−	0.492157i
$52$		0			0
$53$	−4.65994	+	2.37436i	−0.640092	+	0.326143i	−0.743738	−	0.668471i	$-0.766949\pi$
$53$	−4.65994	+	2.37436i	−0.640092	+	0.326143i	0.103646	+	0.994614i	$0.466949\pi$
$54$		0			0
$55$	−6.11942	+	7.57863i	−0.825142	+	1.02190i
$56$		0			0
$57$	1.69044	−	1.69044i	0.223904	−	0.223904i
$58$		0			0
$59$	−0.111573	−	0.0810625i	−0.0145256	−	0.0105534i	0.580499	−	0.814261i	$-0.302858\pi$
$59$	−0.111573	−	0.0810625i	−0.0145256	−	0.0105534i	−0.595024	+	0.803708i	$0.702858\pi$
$60$		0			0
$61$	9.77366	−	7.10098i	1.25139	−	0.909188i	0.253088	−	0.967443i	$-0.418554\pi$
$61$	9.77366	−	7.10098i	1.25139	−	0.909188i	0.998302	+	0.0582557i	$0.0185539\pi$
$62$		0			0
$63$	5.97090	−	0.945698i	0.752263	−	0.119147i
$64$		0			0
$65$	−5.68337	+	2.53999i	−0.704936	+	0.315047i
$66$		0			0
$67$	2.64671	−	5.19446i	0.323347	−	0.634604i	−0.670920	−	0.741530i	$-0.734101\pi$
$67$	2.64671	−	5.19446i	0.323347	−	0.634604i	0.994267	+	0.106926i	$0.0341007\pi$
$68$		0			0
$69$	−3.23305	+	1.05048i	−0.389213	+	0.126463i
$70$		0			0
$71$	−0.559408	−	0.181763i	−0.0663895	−	0.0215712i	0.275634	−	0.961263i	$-0.411112\pi$
$71$	−0.559408	−	0.181763i	−0.0663895	−	0.0215712i	−0.342023	+	0.939691i	$0.611112\pi$
$72$		0			0
$73$	15.0889	+	2.38985i	1.76603	+	0.279711i	0.953100	−	0.302655i	$-0.0978730\pi$
$73$	15.0889	+	2.38985i	1.76603	+	0.279711i	0.812927	+	0.582366i	$0.197873\pi$
$74$		0			0
$75$	−3.39316	−	2.18999i	−0.391808	−	0.252878i
$76$		0			0
$77$	1.75483	−	11.0795i	0.199981	−	1.26263i
$78$		0			0
$79$	−3.31359	+	10.1982i	−0.372808	+	1.14738i	0.572138	+	0.820157i	$0.306114\pi$
$79$	−3.31359	+	10.1982i	−0.372808	+	1.14738i	−0.944946	+	0.327227i	$0.893886\pi$
$80$		0			0
$81$	−1.09829	−	3.38020i	−0.122033	−	0.375578i
$82$		0			0
$83$	0.0483434	+	0.0246322i	0.00530638	+	0.00270374i	0.456642	−	0.889651i	$-0.349052\pi$
$83$	0.0483434	+	0.0246322i	0.00530638	+	0.00270374i	−0.451335	+	0.892354i	$0.649052\pi$
$84$		0			0
$85$	−2.00963	+	9.52042i	−0.217975	+	1.03263i
$86$		0			0
$87$	0.205879	+	1.29987i	0.0220725	+	0.139360i
$88$		0			0
$89$	8.88915	+	12.2349i	0.942248	+	1.29689i	0.954886	+	0.296973i	$0.0959773\pi$
$89$	8.88915	+	12.2349i	0.942248	+	1.29689i	−0.0126374	+	0.999920i	$0.504023\pi$
$90$		0			0
$91$	4.21381	−	5.79981i	0.441727	−	0.607986i
$92$		0			0
$93$	6.00781	+	6.00781i	0.622981	+	0.622981i
$94$		0			0
$95$	−5.54552	+	3.61241i	−0.568959	+	0.370625i
$96$		0			0
$97$	−5.19630	−	10.1983i	−0.527604	−	1.03548i	−0.988948	−	0.148260i	$-0.952633\pi$
$97$	−5.19630	−	10.1983i	−0.527604	−	1.03548i	0.461344	−	0.887221i	$-0.347367\pi$
$98$		0			0
$99$	−10.2267			−1.02782
$100$		0			0
$101$	−14.4256			−1.43540			−0.717698	−	0.696354i	$-0.754804\pi$
$101$	−14.4256			−1.43540			−0.717698	+	0.696354i	$0.754804\pi$
$102$		0			0
$103$	8.37053	+	16.4281i	0.824773	+	1.61871i	0.784997	+	0.619500i	$0.212664\pi$
$103$	8.37053	+	16.4281i	0.824773	+	1.61871i	0.0397759	+	0.999209i	$0.487336\pi$
$104$		0			0
$105$	4.64478	+	0.236870i	0.453284	+	0.0231161i
$106$		0			0
$107$	4.91292	+	4.91292i	0.474950	+	0.474950i	0.903512	−	0.428562i	$-0.140980\pi$
$107$	4.91292	+	4.91292i	0.474950	+	0.474950i	−0.428562	+	0.903512i	$0.640980\pi$
$108$		0			0
$109$	−4.61263	+	6.34874i	−0.441810	+	0.608099i	−0.970613	−	0.240645i	$-0.922641\pi$
$109$	−4.61263	+	6.34874i	−0.441810	+	0.608099i	0.528803	+	0.848744i	$0.322641\pi$
$110$		0			0
$111$	1.58176	+	2.17710i	0.150134	+	0.206641i
$112$		0			0
$113$	1.14268	+	7.21461i	0.107494	+	0.678693i	0.981310	+	0.192435i	$0.0616385\pi$
$113$	1.14268	+	7.21461i	0.107494	+	0.678693i	−0.873815	+	0.486258i	$0.838361\pi$
$114$		0			0
$115$	9.35813	−	0.996894i	0.872650	−	0.0929609i
$116$		0			0
$117$	−5.82333	−	2.96714i	−0.538367	−	0.274312i
$118$		0			0
$119$	−3.46268	−	10.6570i	−0.317424	−	0.976929i
$120$		0			0
$121$	−2.46490	+	7.58617i	−0.224081	+	0.689652i
$122$		0			0
$123$	1.25971	−	7.95347i	0.113584	−	0.717140i
$124$		0			0
$125$	7.93900	+	7.87225i	0.710085	+	0.704116i
$126$		0			0
$127$	−4.84973	−	0.768122i	−0.430344	−	0.0681598i	−0.0624949	−	0.998045i	$-0.519906\pi$
$127$	−4.84973	−	0.768122i	−0.430344	−	0.0681598i	−0.367849	+	0.929885i	$0.619906\pi$
$128$		0			0
$129$	2.19074	+	0.711814i	0.192884	+	0.0626717i
$130$		0			0
$131$	−2.58638	+	0.840365i	−0.225973	+	0.0734231i	−0.419815	−	0.907610i	$-0.637905\pi$
$131$	−2.58638	+	0.840365i	−0.225973	+	0.0734231i	0.193842	+	0.981033i	$0.437905\pi$
$132$		0			0
$133$	3.46021	−	6.79105i	0.300039	−	0.588859i
$134$		0			0
$135$	−1.02307	−	9.60387i	−0.0880521	−	0.826570i
$136$		0			0
$137$	10.0917	−	1.59836i	0.862190	−	0.136557i	0.290348	−	0.956921i	$-0.406229\pi$
$137$	10.0917	−	1.59836i	0.862190	−	0.136557i	0.571842	+	0.820364i	$0.306229\pi$
$138$		0			0
$139$	−18.6778	+	13.5702i	−1.58423	+	1.15101i	−0.672602	+	0.740005i	$0.734823\pi$
$139$	−18.6778	+	13.5702i	−1.58423	+	1.15101i	−0.911632	+	0.411008i	$0.865177\pi$
$140$		0			0
$141$	−0.499453	−	0.362874i	−0.0420615	−	0.0305595i
$142$		0			0
$143$	−8.57546	+	8.57546i	−0.717116	+	0.717116i
$144$		0			0
$145$	0.185564	−	3.63872i	0.0154102	−	0.302179i
$146$		0			0
$147$	0.265486	−	0.135272i	0.0218969	−	0.0111570i
$148$		0			0
$149$			0.198651i			0.0162742i	0.999967	+	0.00813708i	$0.00259014\pi$
$149$			0.198651i			0.0162742i	−0.999967	+	0.00813708i	$0.997410\pi$
$150$		0			0
$151$			8.56486i			0.696999i	0.937309	+	0.348499i	$0.113309\pi$
$151$			8.56486i			0.696999i	−0.937309	+	0.348499i	$0.886691\pi$
$152$		0			0
$153$	−9.10218	+	4.63779i	−0.735868	+	0.374943i
$154$		0			0
$155$	−12.8385	−	19.7087i	−1.03121	−	1.58304i
$156$		0			0
$157$	5.38963	−	5.38963i	0.430139	−	0.430139i	−0.458536	−	0.888676i	$-0.651626\pi$
$157$	5.38963	−	5.38963i	0.430139	−	0.430139i	0.888676	+	0.458536i	$0.151626\pi$
$158$		0			0
$159$	−3.41750	−	2.48296i	−0.271025	−	0.196911i
$160$		0			0
$161$	−8.76809	+	6.37039i	−0.691022	+	0.502057i
$162$		0			0
$163$	−22.0925	+	3.49911i	−1.73042	+	0.274072i	−0.940661	−	0.339347i	$-0.889794\pi$
$163$	−22.0925	+	3.49911i	−1.73042	+	0.274072i	−0.789758	+	0.613418i	$0.789794\pi$
$164$		0			0
$165$	−7.69802	−	1.62495i	−0.599290	−	0.126502i
$166$		0			0
$167$	5.04342	−	9.89826i	0.390271	−	0.765950i	−0.609366	−	0.792889i	$-0.708576\pi$
$167$	5.04342	−	9.89826i	0.390271	−	0.765950i	0.999637	+	0.0269388i	$0.00857592\pi$
$168$		0			0
$169$	4.99261	−	1.62220i	0.384047	−	0.124784i
$170$		0			0
$171$	−6.60841	−	2.14720i	−0.505358	−	0.164201i
$172$		0			0
$173$	15.6169	+	2.47347i	1.18733	+	0.188054i	0.718687	−	0.695334i	$-0.244744\pi$
$173$	15.6169	+	2.47347i	1.18733	+	0.188054i	0.468641	+	0.883388i	$0.344744\pi$
$174$		0			0
$175$	−12.4461	−	3.29740i	−0.940834	−	0.249260i
$176$		0			0
$177$	0.0174255	−	0.110020i	0.00130978	−	0.00826963i
$178$		0			0
$179$	−4.81330	+	14.8138i	−0.359763	+	1.10724i	0.593433	+	0.804884i	$0.297772\pi$
$179$	−4.81330	+	14.8138i	−0.359763	+	1.10724i	−0.953196	+	0.302353i	$0.902228\pi$
$180$		0			0
$181$	−0.982681	−	3.02438i	−0.0730421	−	0.224801i	0.907870	−	0.419252i	$-0.137707\pi$
$181$	−0.982681	−	3.02438i	−0.0730421	−	0.224801i	−0.980912	+	0.194451i	$0.937707\pi$
$182$		0			0
$183$	8.69425	+	4.42994i	0.642698	+	0.327471i
$184$		0			0
$185$	−3.03975	−	6.80162i	−0.223487	−	0.500065i
$186$		0			0
$187$	2.96537	+	18.7226i	0.216849	+	1.36913i
$188$		0			0
$189$	6.53767	+	8.99834i	0.475546	+	0.654533i
$190$		0			0
$191$	14.4163	−	19.8423i	1.04312	−	1.43574i	0.148502	−	0.988912i	$-0.452555\pi$
$191$	14.4163	−	19.8423i	1.04312	−	1.43574i	0.894622	−	0.446824i	$-0.147445\pi$
$192$		0			0
$193$	−1.11728	−	1.11728i	−0.0804236	−	0.0804236i	0.665751	−	0.746174i	$-0.268111\pi$
$193$	−1.11728	−	1.11728i	−0.0804236	−	0.0804236i	−0.746174	+	0.665751i	$0.768111\pi$
$194$		0			0
$195$	−3.91198	−	3.15876i	−0.280143	−	0.226203i
$196$		0			0
$197$	2.80217	+	5.49957i	0.199646	+	0.391828i	0.969024	−	0.246966i	$-0.0794336\pi$
$197$	2.80217	+	5.49957i	0.199646	+	0.391828i	−0.769378	+	0.638794i	$0.779434\pi$
$198$		0			0
$199$	−10.9496			−0.776199			−0.388099	−	0.921618i	$-0.626868\pi$
$199$	−10.9496			−0.776199			−0.388099	+	0.921618i	$0.626868\pi$
$200$		0			0
$201$	4.70881			0.332134
$202$		0			0
$203$	1.90488	+	3.73853i	0.133696	+	0.262394i
$204$		0			0
$205$	−7.95983	+	20.8236i	−0.555939	+	1.45438i
$206$		0			0
$207$	6.98661	+	6.98661i	0.485603	+	0.485603i
$208$		0			0
$209$	−7.57863	+	10.4311i	−0.524225	+	0.721534i
$210$		0			0
$211$	−7.39143	−	10.1734i	−0.508847	−	0.700368i	0.474877	−	0.880052i	$-0.342492\pi$
$211$	−7.39143	−	10.1734i	−0.508847	−	0.700368i	−0.983724	+	0.179684i	$0.942492\pi$
$212$		0			0
$213$	−0.0743200	−	0.469238i	−0.00509233	−	0.0321517i
$214$		0			0
$215$	−5.52714	−	3.18073i	−0.376948	−	0.216924i
$216$		0			0
$217$	24.1354	+	12.2976i	1.63841	+	0.834814i
$218$		0			0
$219$	3.81305	+	11.7354i	0.257662	+	0.793003i
$220$		0			0
$221$	−3.74355	+	11.5215i	−0.251818	+	0.775017i
$222$		0			0
$223$	−4.56640	+	28.8311i	−0.305789	+	1.93068i	0.0560337	+	0.998429i	$0.482155\pi$
$223$	−4.56640	+	28.8311i	−0.305789	+	1.93068i	−0.361823	+	0.932247i	$0.617845\pi$
$224$		0			0
$225$	−1.19411	+	11.6772i	−0.0796071	+	0.778479i
$226$		0			0
$227$	22.7567	+	3.60431i	1.51042	+	0.239226i	0.856026	−	0.516932i	$-0.172926\pi$
$227$	22.7567	+	3.60431i	1.51042	+	0.239226i	0.654389	+	0.756158i	$0.272926\pi$
$228$		0			0
$229$	6.73750	+	2.18915i	0.445227	+	0.144663i	0.523046	−	0.852305i	$-0.324796\pi$
$229$	6.73750	+	2.18915i	0.445227	+	0.144663i	−0.0778192	+	0.996967i	$0.524796\pi$
$230$		0			0
$231$	8.61707	−	2.79985i	0.566961	−	0.184217i
$232$		0			0
$233$	6.63901	−	13.0298i	0.434936	−	0.853609i	−0.564664	−	0.825321i	$-0.690994\pi$
$233$	6.63901	−	13.0298i	0.434936	−	0.853609i	0.999600	−	0.0282886i	$-0.00900573\pi$
$234$		0			0
$235$	1.14540	+	1.26851i	0.0747179	+	0.0827482i
$236$		0			0
$237$	−8.55436	+	1.35488i	−0.555665	+	0.0880087i
$238$		0			0
$239$	5.24208	−	3.80859i	0.339082	−	0.246358i	−0.405192	−	0.914231i	$-0.632795\pi$
$239$	5.24208	−	3.80859i	0.339082	−	0.246358i	0.744274	+	0.667874i	$0.232795\pi$
$240$		0			0
$241$	−5.90034	−	4.28685i	−0.380074	−	0.276140i	0.381302	−	0.924451i	$-0.375476\pi$
$241$	−5.90034	−	4.28685i	−0.380074	−	0.276140i	−0.761376	+	0.648311i	$0.775476\pi$
$242$		0			0
$243$	11.1925	−	11.1925i	0.717998	−	0.717998i
$244$		0			0
$245$	−0.796479	+	0.214617i	−0.0508852	+	0.0137114i
$246$		0			0
$247$	−7.34189	+	3.74088i	−0.467153	+	0.238027i
$248$		0			0
$249$			0.0438236i			0.00277721i
$250$		0			0
$251$			8.97752i			0.566656i	0.959023	+	0.283328i	$0.0914385\pi$
$251$			8.97752i			0.566656i	−0.959023	+	0.283328i	$0.908561\pi$
$252$		0			0
$253$	16.3359	−	8.32358i	1.02703	−	0.523299i
$254$		0			0
$255$	−7.58846	+	2.04477i	−0.475208	+	0.128048i
$256$		0			0
$257$	−16.7559	+	16.7559i	−1.04520	+	1.04520i	−0.0462737	+	0.998929i	$0.514735\pi$
$257$	−16.7559	+	16.7559i	−1.04520	+	1.04520i	−0.998929	+	0.0462737i	$0.985265\pi$
$258$		0			0
$259$	6.94097	+	5.04291i	0.431291	+	0.313351i
$260$		0			0
$261$	3.09466	−	2.24840i	0.191554	−	0.139172i
$262$		0			0
$263$	−22.8477	+	3.61872i	−1.40885	+	0.223140i	−0.814079	−	0.580754i	$-0.802758\pi$
$263$	−22.8477	+	3.61872i	−1.40885	+	0.223140i	−0.594772	+	0.803894i	$0.702758\pi$
$264$		0			0
$265$	7.83741	+	8.67974i	0.481448	+	0.533192i
$266$		0			0
$267$	−5.54549	+	10.8836i	−0.339379	+	0.666068i
$268$		0			0
$269$	13.9626	−	4.53674i	0.851317	−	0.276610i	0.149320	−	0.988789i	$-0.452292\pi$
$269$	13.9626	−	4.53674i	0.851317	−	0.276610i	0.701998	+	0.712179i	$0.252292\pi$
$270$		0			0
$271$	−3.33847	−	1.08473i	−0.202798	−	0.0658929i	0.205857	−	0.978582i	$-0.434002\pi$
$271$	−3.33847	−	1.08473i	−0.202798	−	0.0658929i	−0.408654	+	0.912689i	$0.634002\pi$
$272$		0			0
$273$	5.71910	+	0.905817i	0.346136	+	0.0548225i
$274$		0			0
$275$	19.9228	+	8.80312i	1.20139	+	0.530848i
$276$		0			0
$277$	1.86639	−	11.7839i	0.112141	−	0.708028i	−0.865994	−	0.500055i	$-0.833313\pi$
$277$	1.86639	−	11.7839i	0.112141	−	0.708028i	0.978134	−	0.207973i	$-0.0666868\pi$
$278$		0			0
$279$	7.63114	−	23.4862i	0.456864	−	1.40608i
$280$		0			0
$281$	−8.07464	−	24.8512i	−0.481693	−	1.48250i	−0.836714	−	0.547640i	$-0.815526\pi$
$281$	−8.07464	−	24.8512i	−0.481693	−	1.48250i	0.355021	−	0.934858i	$-0.384474\pi$
$282$		0			0
$283$	11.1310	+	5.67151i	0.661667	+	0.337136i	0.752369	−	0.658742i	$-0.228911\pi$
$283$	11.1310	+	5.67151i	0.661667	+	0.337136i	−0.0907018	+	0.995878i	$0.528911\pi$
$284$		0			0
$285$	−4.63322	−	2.66630i	−0.274448	−	0.157938i
$286$		0			0
$287$	−4.01615	−	25.3570i	−0.237066	−	1.49678i
$288$		0			0
$289$	1.13761	+	1.56579i	0.0669182	+	0.0921050i
$290$		0			0
$291$	5.43397	−	7.47922i	0.318545	−	0.438440i
$292$		0			0
$293$	−5.15186	−	5.15186i	−0.300975	−	0.300975i	0.540420	−	0.841395i	$-0.318265\pi$
$293$	−5.15186	−	5.15186i	−0.300975	−	0.300975i	−0.841395	+	0.540420i	$0.818265\pi$
$294$		0			0
$295$	−0.110108	+	0.288053i	−0.00641076	+	0.0167711i
$296$		0			0
$297$	−8.54215	−	16.7649i	−0.495666	−	0.972799i
$298$		0			0
$299$	11.7170			0.677614
$300$		0			0
$301$	7.34388			0.423294
$302$		0			0
$303$	−5.28970	−	10.3816i	−0.303885	−	0.596408i
$304$		0			0
$305$	−21.0175	−	16.9707i	−1.20346	−	0.971742i
$306$		0			0
$307$	9.16571	+	9.16571i	0.523115	+	0.523115i	0.918511	−	0.395396i	$-0.129393\pi$
$307$	9.16571	+	9.16571i	0.523115	+	0.523115i	−0.395396	+	0.918511i	$0.629393\pi$
$308$		0			0
$309$	−8.75339	+	12.0480i	−0.497963	+	0.685388i
$310$		0			0
$311$	5.82649	+	8.01948i	0.330390	+	0.454743i	0.941604	−	0.336722i	$-0.109318\pi$
$311$	5.82649	+	8.01948i	0.330390	+	0.454743i	−0.611214	+	0.791466i	$0.709318\pi$
$312$		0			0
$313$	1.37344	+	8.67156i	0.0776314	+	0.490145i	0.995616	+	0.0935304i	$0.0298152\pi$
$313$	1.37344	+	8.67156i	0.0776314	+	0.490145i	−0.917985	+	0.396615i	$0.870185\pi$
$314$		0			0
$315$	−5.51554	−	12.3413i	−0.310766	−	0.695356i
$316$		0			0
$317$	6.55936	+	3.34216i	0.368410	+	0.187714i	0.628388	−	0.777900i	$-0.283715\pi$
$317$	6.55936	+	3.34216i	0.368410	+	0.187714i	−0.259978	+	0.965615i	$0.583715\pi$
$318$		0			0
$319$	−2.19340	−	6.75061i	−0.122807	−	0.377961i
$320$		0			0
$321$	−1.73416	+	5.33719i	−0.0967913	+	0.297893i
$322$		0			0
$323$	−2.01481	+	12.7210i	−0.112107	+	0.707815i
$324$		0			0
$325$	8.79044	+	10.7930i	0.487606	+	0.598690i
$326$		0			0
$327$	−6.26039	−	0.991548i	−0.346200	−	0.0548327i
$328$		0			0
$329$	−1.87191	−	0.608219i	−0.103202	−	0.0335322i
$330$		0			0
$331$	−25.0641	+	8.14381i	−1.37765	+	0.447624i	−0.901895	−	0.431955i	$-0.857824\pi$
$331$	−25.0641	+	8.14381i	−1.37765	+	0.447624i	−0.475751	+	0.879580i	$0.657824\pi$
$332$		0			0
$333$	3.55094	−	6.96912i	0.194590	−	0.381905i
$334$		0			0
$335$	−12.7549	−	2.69239i	−0.696876	−	0.147101i
$336$		0			0
$337$	1.36532	−	0.216246i	0.0743738	−	0.0117796i	−0.119137	−	0.992878i	$-0.538013\pi$
$337$	1.36532	−	0.216246i	0.0743738	−	0.0117796i	0.193510	+	0.981098i	$0.438013\pi$
$338$		0			0
$339$	−4.77312	+	3.46787i	−0.259240	+	0.188349i
$340$		0			0
$341$	−37.0720	−	26.9344i	−2.00756	−	1.45858i
$342$		0			0
$343$	13.4178	−	13.4178i	0.724492	−	0.724492i
$344$		0			0
$345$	4.14896	+	6.36920i	0.223373	+	0.342906i
$346$		0			0
$347$	23.9810	−	12.2189i	1.28737	−	0.655946i	0.329770	−	0.944061i	$-0.393029\pi$
$347$	23.9810	−	12.2189i	1.28737	−	0.655946i	0.957596	+	0.288116i	$0.0930287\pi$
$348$		0			0
$349$			28.2766i			1.51361i	0.653639	+	0.756806i	$0.273241\pi$
$349$			28.2766i			1.51361i	−0.653639	+	0.756806i	$0.726759\pi$
$350$		0			0
$351$		−	12.0247i		−	0.641833i
$352$		0			0
$353$	11.3849	−	5.80091i	0.605959	−	0.308751i	−0.123958	−	0.992287i	$-0.539559\pi$
$353$	11.3849	−	5.80091i	0.605959	−	0.308751i	0.729917	+	0.683536i	$0.239559\pi$
$354$		0			0
$355$	−0.0669864	+	1.31354i	−0.00355527	+	0.0697154i
$356$		0			0
$357$	6.39980	−	6.39980i	0.338714	−	0.338714i
$358$		0			0
$359$	−1.56898	−	1.13993i	−0.0828078	−	0.0601634i	0.545611	−	0.838039i	$-0.316298\pi$
$359$	−1.56898	−	1.13993i	−0.0828078	−	0.0601634i	−0.628419	+	0.777875i	$0.716298\pi$
$360$		0			0
$361$	8.28396	−	6.01865i	0.435998	−	0.316771i
$362$		0			0
$363$	−6.36338	+	1.00786i	−0.333991	+	0.0528989i
$364$		0			0
$365$	−3.61854	−	33.9683i	−0.189403	−	1.77798i
$366$		0			0
$367$	12.1323	−	23.8109i	0.633299	−	1.24292i	−0.321849	−	0.946791i	$-0.604304\pi$
$367$	12.1323	−	23.8109i	0.633299	−	1.24292i	0.955148	−	0.296129i	$-0.0956958\pi$
$368$		0			0
$369$	−22.2597	+	7.23260i	−1.15879	+	0.376514i
$370$		0			0
$371$	−12.8085	−	4.16173i	−0.664984	−	0.216066i
$372$		0			0
$373$	−21.1611	−	3.35159i	−1.09568	−	0.173539i	−0.417676	−	0.908596i	$-0.637155\pi$
$373$	−21.1611	−	3.35159i	−1.09568	−	0.173539i	−0.678005	+	0.735057i	$0.737155\pi$
$374$		0			0
$375$	−2.75427	+	8.60011i	−0.142230	+	0.444108i
$376$		0			0
$377$	0.709616	−	4.48034i	0.0365471	−	0.230749i
$378$		0			0
$379$	−1.09116	+	3.35824i	−0.0560490	+	0.172501i	−0.975162	−	0.221493i	$-0.928907\pi$
$379$	−1.09116	+	3.35824i	−0.0560490	+	0.172501i	0.919113	+	0.393994i	$0.128907\pi$
$380$		0			0
$381$	−1.22555	−	3.77186i	−0.0627869	−	0.193238i
$382$		0			0
$383$	14.5309	+	7.40386i	0.742494	+	0.378320i	0.783953	−	0.620821i	$-0.213200\pi$
$383$	14.5309	+	7.40386i	0.742494	+	0.378320i	−0.0414587	+	0.999140i	$0.513200\pi$
$384$		0			0
$385$	−24.9423	+	2.65703i	−1.27118	+	0.135415i
$386$		0			0
$387$	−1.04735	−	6.61271i	−0.0532398	−	0.336143i
$388$		0			0
$389$	−7.07344	−	9.73575i	−0.358638	−	0.493622i	0.591131	−	0.806576i	$-0.298682\pi$
$389$	−7.07344	−	9.73575i	−0.358638	−	0.493622i	−0.949768	+	0.312953i	$0.898682\pi$
$390$		0			0
$391$	10.7649	−	14.8166i	0.544405	−	0.749309i
$392$		0			0
$393$	−1.55318	−	1.55318i	−0.0783477	−	0.0783477i
$394$		0			0
$395$	23.9462	+	1.22118i	1.20486	+	0.0614444i
$396$		0			0
$397$	−4.87032	−	9.55855i	−0.244435	−	0.479730i	0.735895	−	0.677095i	$-0.236761\pi$
$397$	−4.87032	−	9.55855i	−0.244435	−	0.479730i	−0.980330	+	0.197365i	$0.936761\pi$
$398$		0			0
$399$	6.15613			0.308192
$400$		0			0
$401$	25.1243			1.25465			0.627324	−	0.778758i	$-0.284150\pi$
$401$	25.1243			1.25465			0.627324	+	0.778758i	$0.284150\pi$
$402$		0			0
$403$	−13.2951	−	26.0930i	−0.662274	−	1.29979i
$404$		0			0
$405$	−6.65909	+	4.33780i	−0.330893	+	0.215547i
$406$		0			0
$407$	−10.2627	−	10.2627i	−0.508705	−	0.508705i
$408$		0			0
$409$	12.3360	−	16.9790i	0.609974	−	0.839557i	−0.386601	−	0.922247i	$-0.626351\pi$
$409$	12.3360	−	16.9790i	0.609974	−	0.839557i	0.996575	+	0.0826897i	$0.0263510\pi$
$410$		0			0
$411$	4.85080	+	6.67656i	0.239272	+	0.329330i
$412$		0			0
$413$	−0.0555554	−	0.350763i	−0.00273370	−	0.0172599i
$414$		0			0
$415$	0.0250574	−	0.118707i	0.00123002	−	0.00582708i
$416$		0			0
$417$	−16.6150	−	8.46578i	−0.813642	−	0.414571i
$418$		0			0
$419$	8.30723	+	25.5670i	0.405835	+	1.24903i	0.920196	+	0.391458i	$0.128029\pi$
$419$	8.30723	+	25.5670i	0.405835	+	1.24903i	−0.514361	+	0.857574i	$0.671971\pi$
$420$		0			0
$421$	−2.41186	+	7.42295i	−0.117547	+	0.361772i	−0.992470	−	0.122490i	$-0.960912\pi$
$421$	−2.41186	+	7.42295i	−0.117547	+	0.361772i	0.874923	+	0.484262i	$0.160912\pi$
$422$		0			0
$423$	−0.280701	+	1.77228i	−0.0136482	+	0.0861712i
$424$		0			0
$425$	21.7243	−	1.19984i	1.05378	−	0.0582006i
$426$		0			0
$427$	30.7265	+	4.86659i	1.48696	+	0.235511i
$428$		0			0
$429$	−9.31602	−	3.02696i	−0.449782	−	0.146143i
$430$		0			0
$431$	13.8852	−	4.51156i	0.668825	−	0.217314i	0.0451287	−	0.998981i	$-0.485630\pi$
$431$	13.8852	−	4.51156i	0.668825	−	0.217314i	0.623696	+	0.781667i	$0.285630\pi$
$432$		0			0
$433$	1.29950	−	2.55042i	0.0624501	−	0.122565i	−0.857671	−	0.514198i	$-0.828090\pi$
$433$	1.29950	−	2.55042i	0.0624501	−	0.122565i	0.920122	+	0.391633i	$0.128090\pi$
$434$		0			0
$435$	2.68672	−	1.20074i	0.128818	−	0.0575709i
$436$		0			0
$437$	12.3038	−	1.94872i	0.588569	−	0.0932201i
$438$		0			0
$439$	16.0330	−	11.6486i	0.765212	−	0.555959i	−0.135293	−	0.990806i	$-0.543198\pi$
$439$	16.0330	−	11.6486i	0.765212	−	0.555959i	0.900504	+	0.434847i	$0.143198\pi$
$440$		0			0
$441$	−0.700639	−	0.509044i	−0.0333638	−	0.0242402i
$442$		0			0
$443$	−1.51430	+	1.51430i	−0.0719466	+	0.0719466i	−0.742164	−	0.670218i	$-0.766201\pi$
$443$	−1.51430	+	1.51430i	−0.0719466	+	0.0719466i	0.670218	+	0.742164i	$0.266201\pi$
$444$		0			0
$445$	21.2443	−	26.3102i	1.00708	−	1.24722i
$446$		0			0
$447$	−0.142963	+	0.0728434i	−0.00676193	+	0.00344537i
$448$		0			0
$449$			3.84719i			0.181560i	0.995871	+	0.0907801i	$0.0289360\pi$
$449$			3.84719i			0.181560i	−0.995871	+	0.0907801i	$0.971064\pi$
$450$		0			0
$451$			43.4304i			2.04506i
$452$		0			0
$453$	−6.16386	+	3.14064i	−0.289603	+	0.147560i
$454$		0			0
$455$	−14.9736	−	5.72368i	−0.701975	−	0.268330i
$456$		0			0
$457$	14.1536	−	14.1536i	0.662077	−	0.662077i	−0.293792	−	0.955869i	$-0.594917\pi$
$457$	14.1536	−	14.1536i	0.662077	−	0.662077i	0.955869	+	0.293792i	$0.0949173\pi$
$458$		0			0
$459$	−15.2057	−	11.0476i	−0.709742	−	0.515658i
$460$		0			0
$461$	−6.34755	+	4.61177i	−0.295635	+	0.214791i	−0.725708	−	0.688003i	$-0.758488\pi$
$461$	−6.34755	+	4.61177i	−0.295635	+	0.214791i	0.430073	+	0.902794i	$0.358488\pi$
$462$		0			0
$463$	17.7982	−	2.81895i	0.827151	−	0.131008i	0.271516	−	0.962434i	$-0.412475\pi$
$463$	17.7982	−	2.81895i	0.827151	−	0.131008i	0.555635	+	0.831426i	$0.312475\pi$
$464$		0			0
$465$	9.47603	−	16.4664i	0.439440	−	0.763612i
$466$		0			0
$467$	−17.3481	+	34.0476i	−0.802776	+	1.57554i	0.0149220	+	0.999889i	$0.495250\pi$
$467$	−17.3481	+	34.0476i	−0.802776	+	1.57554i	−0.817698	+	0.575648i	$0.804750\pi$
$468$		0			0
$469$	14.2777	−	4.63911i	0.659283	−	0.214214i
$470$		0			0
$471$	5.85507	+	1.90243i	0.269787	+	0.0876592i
$472$		0			0
$473$	−12.2705	−	1.94345i	−0.564197	−	0.0893600i
$474$		0			0
$475$	11.0257	+	9.87150i	0.505892	+	0.452935i
$476$		0			0
$477$	−1.92070	+	12.1268i	−0.0879426	+	0.555248i
$478$		0			0
$479$	0.417095	−	1.28369i	0.0190576	−	0.0586531i	−0.941075	−	0.338197i	$-0.890183\pi$
$479$	0.417095	−	1.28369i	0.0190576	−	0.0586531i	0.960133	+	0.279543i	$0.0901831\pi$
$480$		0			0
$481$	−2.86626	−	8.82145i	−0.130690	−	0.402223i
$482$		0			0
$483$	−7.79973	−	3.97416i	−0.354900	−	0.180831i
$484$		0			0
$485$	−18.9957	+	17.1522i	−0.862549	+	0.778843i
$486$		0			0
$487$	2.41262	+	15.2327i	0.109326	+	0.690259i	0.980090	+	0.198556i	$0.0636252\pi$
$487$	2.41262	+	15.2327i	0.109326	+	0.690259i	−0.870763	+	0.491702i	$0.836375\pi$
$488$		0			0
$489$	−10.6193	−	14.6162i	−0.480221	−	0.660967i
$490$		0			0
$491$	24.7615	−	34.0812i	1.11747	−	1.53806i	0.307541	−	0.951535i	$-0.400494\pi$
$491$	24.7615	−	34.0812i	1.11747	−	1.53806i	0.809928	−	0.586529i	$-0.199506\pi$
$492$		0			0
$493$	−5.01360	−	5.01360i	−0.225801	−	0.225801i
$494$		0			0
$495$	5.94965	+	22.0801i	0.267417	+	0.992426i
$496$		0			0
$497$	−0.687641	−	1.34957i	−0.0308449	−	0.0605365i
$498$		0			0
$499$	−24.0843			−1.07816			−0.539081	−	0.842254i	$-0.681228\pi$
$499$	−24.0843			−1.07816			−0.539081	+	0.842254i	$0.681228\pi$
$500$		0			0
$501$	8.97283			0.400877
$502$		0			0
$503$	−9.76105	−	19.1571i	−0.435224	−	0.854174i	−0.999590	−	0.0286495i	$-0.990879\pi$
$503$	−9.76105	−	19.1571i	−0.435224	−	0.854174i	0.564366	−	0.825525i	$-0.309121\pi$
$504$		0			0
$505$	8.39244	+	31.1456i	0.373459	+	1.38596i
$506$		0			0
$507$	2.99818	+	2.99818i	0.133154	+	0.133154i
$508$		0			0
$509$	16.7370	−	23.0365i	0.741856	−	1.02108i	−0.256654	−	0.966503i	$-0.582620\pi$
$509$	16.7370	−	23.0365i	0.741856	−	1.02108i	0.998510	−	0.0545733i	$-0.0173799\pi$
$510$		0			0
$511$	23.1233	+	31.8265i	1.02292	+	1.40792i
$512$		0			0
$513$	−1.99990	−	12.6269i	−0.0882976	−	0.557489i
$514$		0			0
$515$	30.5995	−	27.6299i	1.34837	−	1.21752i
$516$		0			0
$517$	2.96671	+	1.51161i	0.130476	+	0.0664807i
$518$		0			0
$519$	3.94646	+	12.1460i	0.173230	+	0.533148i
$520$		0			0
$521$	−6.95785	+	21.4141i	−0.304829	+	0.938167i	0.674912	+	0.737898i	$0.264182\pi$
$521$	−6.95785	+	21.4141i	−0.304829	+	0.938167i	−0.979741	+	0.200269i	$0.935818\pi$
$522$		0			0
$523$	1.25652	−	7.93336i	0.0549438	−	0.346902i	−0.944867	−	0.327454i	$-0.893809\pi$
$523$	1.25652	−	7.93336i	0.0549438	−	0.346902i	0.999811	−	0.0194475i	$-0.00619071\pi$
$524$		0			0
$525$	−2.19080	−	10.1662i	−0.0956146	−	0.443688i
$526$		0			0
$527$	−45.2103	−	7.16061i	−1.96939	−	0.311921i
$528$		0			0
$529$	5.02759	+	1.63356i	0.218591	+	0.0710244i
$530$		0			0
$531$	−0.307918	+	0.100049i	−0.0133625	+	0.00434174i
$532$		0			0
$533$	−12.6007	+	24.7303i	−0.545798	+	1.07119i
$534$		0			0
$535$	7.74907	−	13.4655i	0.335022	−	0.582165i
$536$		0			0
$537$	−12.4260	+	1.96809i	−0.536223	+	0.0849293i
$538$		0			0
$539$	−1.30010	+	0.944576i	−0.0559992	+	0.0406858i
$540$		0			0
$541$	25.5113	+	18.5351i	1.09682	+	0.796885i	0.980538	−	0.196332i	$-0.0629030\pi$
$541$	25.5113	+	18.5351i	1.09682	+	0.796885i	0.116280	+	0.993216i	$0.462903\pi$
$542$		0			0
$543$	1.81621	−	1.81621i	0.0779412	−	0.0779412i
$544$		0			0
$545$	16.3908	+	6.26540i	0.702106	+	0.268380i
$546$		0			0
$547$	−12.7018	+	6.47188i	−0.543089	+	0.276718i	−0.703938	−	0.710261i	$-0.748577\pi$
$547$	−12.7018	+	6.47188i	−0.543089	+	0.276718i	0.160849	+	0.986979i	$0.448577\pi$
$548$		0			0
$549$		−	28.3614i		−	1.21043i
$550$		0			0
$551$		−	4.82271i		−	0.205454i
$552$		0			0
$553$	−24.6031	+	12.5359i	−1.04623	+	0.533081i
$554$		0			0
$555$	3.78027	−	4.68169i	0.160463	−	0.198727i
$556$		0			0
$557$	−32.6995	+	32.6995i	−1.38552	+	1.38552i	−0.551045	+	0.834475i	$0.685771\pi$
$557$	−32.6995	+	32.6995i	−1.38552	+	1.38552i	−0.834475	+	0.551045i	$0.814229\pi$
$558$		0			0
$559$	−6.42324	−	4.66675i	−0.271674	−	0.197383i
$560$		0			0
$561$	−12.3867	+	8.99946i	−0.522967	+	0.379958i
$562$		0			0
$563$	31.4298	−	4.97800i	1.32461	−	0.209798i	0.546253	−	0.837620i	$-0.316054\pi$
$563$	31.4298	−	4.97800i	1.32461	−	0.209798i	0.778356	+	0.627823i	$0.216054\pi$
$564$		0			0
$565$	14.9120	−	6.66440i	0.627352	−	0.280373i
$566$		0			0
$567$	4.15504	−	8.15473i	0.174495	−	0.342467i
$568$		0			0
$569$	4.41879	−	1.43575i	0.185245	−	0.0601898i	−0.214925	−	0.976630i	$-0.568951\pi$
$569$	4.41879	−	1.43575i	0.185245	−	0.0601898i	0.400171	+	0.916441i	$0.368951\pi$
$570$		0			0
$571$	−39.0676	−	12.6938i	−1.63493	−	0.531221i	−0.659533	−	0.751676i	$-0.729246\pi$
$571$	−39.0676	−	12.6938i	−1.63493	−	0.531221i	−0.975397	+	0.220455i	$0.929246\pi$
$572$		0			0
$573$	19.5661	+	3.09897i	0.817387	+	0.129461i
$574$		0			0
$575$	−7.59669	−	19.6248i	−0.316804	−	0.818410i
$576$		0			0
$577$	−0.454561	+	2.86999i	−0.0189236	+	0.119479i	−0.995342	−	0.0964085i	$-0.969264\pi$
$577$	−0.454561	+	2.86999i	−0.0189236	+	0.119479i	0.976418	+	0.215888i	$0.0692645\pi$
$578$		0			0
$579$	0.394377	−	1.21377i	0.0163897	−	0.0504424i
$580$		0			0
$581$	0.0431749	+	0.132879i	0.00179120	+	0.00551274i
$582$		0			0
$583$	20.2997	+	10.3432i	0.840726	+	0.428371i
$584$		0			0
$585$	−3.01835	+	14.2991i	−0.124793	+	0.591196i
$586$		0			0
$587$	−6.09697	−	38.4948i	−0.251649	−	1.58885i	−0.712695	−	0.701474i	$-0.752526\pi$
$587$	−6.09697	−	38.4948i	−0.251649	−	1.58885i	0.461046	−	0.887376i	$-0.347474\pi$
$588$		0			0
$589$	−18.3005	−	25.1884i	−0.754058	−	1.03787i
$590$		0			0
$591$	−2.93034	+	4.03326i	−0.120538	+	0.165906i
$592$		0			0
$593$	−18.0163	−	18.0163i	−0.739841	−	0.739841i	0.232706	−	0.972547i	$-0.425242\pi$
$593$	−18.0163	−	18.0163i	−0.739841	−	0.739841i	−0.972547	+	0.232706i	$0.925242\pi$
$594$		0			0
$595$	−20.9947	+	13.6761i	−0.860698	+	0.560667i
$596$		0			0
$597$	−4.01511	−	7.88010i	−0.164328	−	0.322511i
$598$		0			0
$599$	18.6484			0.761954			0.380977	−	0.924584i	$-0.375588\pi$
$599$	18.6484			0.761954			0.380977	+	0.924584i	$0.375588\pi$
$600$		0			0
$601$	5.17725			0.211185			0.105592	−	0.994410i	$-0.466326\pi$
$601$	5.17725			0.211185			0.105592	+	0.994410i	$0.466326\pi$
$602$		0			0
$603$	−6.21346	−	12.1946i	−0.253032	−	0.496602i
$604$		0			0
$605$	17.8130	+	0.908408i	0.724201	+	0.0369320i
$606$		0			0
$607$	15.3417	+	15.3417i	0.622699	+	0.622699i	0.946221	−	0.323522i	$-0.104867\pi$
$607$	15.3417	+	15.3417i	0.622699	+	0.622699i	−0.323522	+	0.946221i	$0.604867\pi$
$608$		0			0
$609$	−1.99201	+	2.74176i	−0.0807201	+	0.111102i
$610$		0			0
$611$	1.25074	+	1.72150i	0.0505996	+	0.0696443i
$612$		0			0
$613$	6.85933	+	43.3081i	0.277046	+	1.74920i	0.597440	+	0.801914i	$0.296185\pi$
$613$	6.85933	+	43.3081i	0.277046	+	1.74920i	−0.320394	+	0.947284i	$0.603815\pi$
$614$		0			0
$615$	−17.9049	+	1.90735i	−0.721994	+	0.0769119i
$616$		0			0
$617$	8.27520	+	4.21643i	0.333147	+	0.169747i	0.612560	−	0.790424i	$-0.290140\pi$
$617$	8.27520	+	4.21643i	0.333147	+	0.169747i	−0.279413	+	0.960171i	$0.590140\pi$
$618$		0			0
$619$	−0.484521	−	1.49120i	−0.0194745	−	0.0599365i	0.940847	−	0.338832i	$-0.110032\pi$
$619$	−0.484521	−	1.49120i	−0.0194745	−	0.0599365i	−0.960322	+	0.278895i	$0.910032\pi$
$620$		0			0
$621$	−5.61757	+	17.2891i	−0.225425	+	0.693788i
$622$		0			0
$623$	−6.09210	+	38.4640i	−0.244075	+	1.54103i
$624$		0			0
$625$	12.3779	−	21.7206i	0.495118	−	0.868826i
$626$		0			0
$627$	−10.2859	−	1.62913i	−0.410781	−	0.0650613i
$628$		0			0
$629$	−13.7884	−	4.48012i	−0.549779	−	0.178634i
$630$		0			0
$631$	0.573929	−	0.186481i	0.0228477	−	0.00742368i	−0.297571	−	0.954700i	$-0.596176\pi$
$631$	0.573929	−	0.186481i	0.0228477	−	0.00742368i	0.320419	+	0.947276i	$0.396176\pi$
$632$		0			0
$633$	4.61114	−	9.04986i	0.183276	−	0.359700i
$634$		0			0
$635$	1.16303	+	10.9177i	0.0461536	+	0.433257i
$636$		0			0
$637$	−1.01436	+	0.160659i	−0.0401905	+	0.00636555i
$638$		0			0
$639$	−1.11714	+	0.811648i	−0.0441933	+	0.0321083i
$640$		0			0
$641$	2.49965	+	1.81610i	0.0987304	+	0.0717318i	0.636055	−	0.771644i	$-0.280565\pi$
$641$	2.49965	+	1.81610i	0.0987304	+	0.0717318i	−0.537325	+	0.843375i	$0.680565\pi$
$642$		0			0
$643$	4.70888	−	4.70888i	0.185700	−	0.185700i	−0.608134	−	0.793834i	$-0.708082\pi$
$643$	4.70888	−	4.70888i	0.185700	−	0.185700i	0.793834	+	0.608134i	$0.208082\pi$
$644$		0			0
$645$	0.262331	−	5.14405i	0.0103293	−	0.202547i
$646$		0			0
$647$	−26.7468	+	13.6282i	−1.05152	+	0.535778i	−0.892290	−	0.451462i	$-0.850902\pi$
$647$	−26.7468	+	13.6282i	−1.05152	+	0.535778i	−0.159234	+	0.987241i	$0.550902\pi$
$648$		0			0
$649$			0.600773i			0.0235824i
$650$		0			0
$651$			21.8788i			0.857499i
$652$		0			0
$653$	−17.5241	+	8.92896i	−0.685770	+	0.349417i	−0.761913	−	0.647680i	$-0.775739\pi$
$653$	−17.5241	+	8.92896i	−0.685770	+	0.349417i	0.0761430	+	0.997097i	$0.475739\pi$
$654$		0			0
$655$	3.31909	+	5.09524i	0.129688	+	0.199088i
$656$		0			0
$657$	25.3601	−	25.3601i	0.989392	−	0.989392i
$658$		0			0
$659$	8.34120	+	6.06024i	0.324927	+	0.236073i	0.738275	−	0.674500i	$-0.235641\pi$
$659$	8.34120	+	6.06024i	0.324927	+	0.236073i	−0.413348	+	0.910573i	$0.635641\pi$
$660$		0			0
$661$	19.0061	−	13.8088i	0.739252	−	0.537098i	−0.153224	−	0.988191i	$-0.548966\pi$
$661$	19.0061	−	13.8088i	0.739252	−	0.537098i	0.892477	+	0.451093i	$0.148966\pi$
$662$		0			0
$663$	−9.66435	+	1.53068i	−0.375332	+	0.0594468i
$664$		0			0
$665$	−16.6754	−	3.51994i	−0.646642	−	0.136497i
$666$		0			0
$667$	−3.11336	+	6.11030i	−0.120550	+	0.236592i
$668$		0			0
$669$	−22.4233	+	7.28577i	−0.866935	+	0.281684i
$670$		0			0
$671$	−50.0513	−	16.2626i	−1.93221	−	0.627812i
$672$		0			0
$673$	27.6047	+	4.37215i	1.06408	+	0.168534i	0.663839	−	0.747875i	$-0.268926\pi$
$673$	27.6047	+	4.37215i	1.06408	+	0.168534i	0.400243	+	0.916409i	$0.368926\pi$
$674$		0			0
$675$	−20.1401	+	7.79617i	−0.775194	+	0.300075i
$676$		0			0
$677$	−5.47504	+	34.5680i	−0.210423	+	1.32856i	0.625721	+	0.780047i	$0.284805\pi$
$677$	−5.47504	+	34.5680i	−0.210423	+	1.32856i	−0.836144	+	0.548510i	$0.815195\pi$
$678$		0			0
$679$	9.10799	−	28.0315i	0.349533	−	1.07575i
$680$		0			0
$681$	5.75073	+	17.6989i	0.220369	+	0.678225i
$682$		0			0
$683$	−0.589867	−	0.300552i	−0.0225706	−	0.0115003i	0.442669	−	0.896685i	$-0.354032\pi$
$683$	−0.589867	−	0.300552i	−0.0225706	−	0.0115003i	−0.465239	+	0.885185i	$0.654032\pi$
$684$		0			0
$685$	−9.32205	−	20.8586i	−0.356177	−	0.796967i
$686$		0			0
$687$	0.895110	+	5.65150i	0.0341506	+	0.215618i
$688$		0			0
$689$	8.55818	+	11.7793i	0.326041	+	0.448757i
$690$		0			0
$691$	1.36289	−	1.87586i	0.0518468	−	0.0713610i	−0.782306	−	0.622894i	$-0.785957\pi$
$691$	1.36289	−	1.87586i	0.0518468	−	0.0713610i	0.834153	+	0.551533i	$0.185957\pi$
$692$		0			0
$693$	−18.6215	−	18.6215i	−0.707371	−	0.707371i
$694$		0			0
$695$	40.1653	+	32.4317i	1.52356	+	1.23021i
$696$		0			0
$697$	19.6956	+	38.6548i	0.746024	+	1.46415i
$698$		0			0
$699$	11.8116			0.446755
$700$		0			0
$701$	37.6668			1.42265			0.711327	−	0.702861i	$-0.248094\pi$
$701$	37.6668			1.42265			0.711327	+	0.702861i	$0.248094\pi$
$702$		0			0
$703$	−4.47693	−	8.78646i	−0.168850	−	0.331388i
$704$		0			0
$705$	−0.492896	+	1.28946i	−0.0185635	+	0.0485638i
$706$		0			0
$707$	−26.2670	−	26.2670i	−0.987872	−	0.987872i
$708$		0			0
$709$	−0.151208	+	0.208120i	−0.00567875	+	0.00781612i	−0.811847	−	0.583870i	$-0.801538\pi$
$709$	−0.151208	+	0.208120i	−0.00567875	+	0.00781612i	0.806168	+	0.591686i	$0.201538\pi$
$710$		0			0
$711$	14.7966	+	20.3658i	0.554916	+	0.763776i
$712$		0			0
$713$	6.92575	+	43.7275i	0.259371	+	1.63761i
$714$		0			0
$715$	23.5039	+	13.5259i	0.878997	+	0.505841i
$716$		0			0
$717$	4.66314	+	2.37599i	0.174148	+	0.0887329i
$718$		0			0
$719$	−9.84670	−	30.3050i	−0.367220	−	1.13019i	−0.948579	−	0.316539i	$-0.897479\pi$
$719$	−9.84670	−	30.3050i	−0.367220	−	1.13019i	0.581360	−	0.813647i	$-0.302521\pi$
$720$		0			0
$721$	−14.6717	+	45.1550i	−0.546404	+	1.68166i
$722$		0			0
$723$	0.921517	−	5.81823i	0.0342716	−	0.216382i
$724$		0			0
$725$	−7.96417	+	1.71628i	−0.295782	+	0.0637409i
$726$		0			0
$727$	−44.0672	−	6.97956i	−1.63436	−	0.258858i	−0.729318	−	0.684175i	$-0.760163\pi$
$727$	−44.0672	−	6.97956i	−1.63436	−	0.258858i	−0.905044	+	0.425317i	$0.860163\pi$
$728$		0			0
$729$	2.01843	+	0.655829i	0.0747568	+	0.0242900i
$730$		0			0
$731$	−11.8026	+	3.83489i	−0.436534	+	0.141838i
$732$		0			0
$733$	9.81751	−	19.2679i	0.362618	−	0.711678i	−0.635558	−	0.772053i	$-0.719230\pi$
$733$	9.81751	−	19.2679i	0.362618	−	0.711678i	0.998176	+	0.0603754i	$0.0192298\pi$
$734$		0			0
$735$	−0.446514	−	0.494503i	−0.0164699	−	0.0182400i
$736$		0			0
$737$	−25.0835	+	3.97284i	−0.923963	+	0.146341i
$738$		0			0
$739$	42.7220	−	31.0394i	1.57155	−	1.14180i	0.645906	−	0.763417i	$-0.276480\pi$
$739$	42.7220	−	31.0394i	1.57155	−	1.14180i	0.925649	−	0.378385i	$-0.123520\pi$
$740$		0			0
$741$	−5.38439	−	3.91199i	−0.197800	−	0.143710i
$742$		0			0
$743$	−7.89430	+	7.89430i	−0.289614	+	0.289614i	−0.836927	−	0.547314i	$-0.815650\pi$
$743$	−7.89430	+	7.89430i	−0.289614	+	0.289614i	0.547314	+	0.836927i	$0.315650\pi$
$744$		0			0
$745$	0.428900	−	0.115571i	0.0157137	−	0.00423418i
$746$		0			0
$747$	0.113492	−	0.0578270i	0.00415245	−	0.00211578i
$748$		0			0
$749$			17.8915i			0.653742i
$750$		0			0
$751$			45.8639i			1.67360i	0.547511	+	0.836798i	$0.315575\pi$
$751$			45.8639i			1.67360i	−0.547511	+	0.836798i	$0.684425\pi$
$752$		0			0
$753$	−6.46084	+	3.29196i	−0.235446	+	0.119966i
$754$		0			0
$755$	18.4921	−	4.98283i	0.672995	−	0.181344i
$756$		0			0
$757$	−25.5537	+	25.5537i	−0.928765	+	0.928765i	−0.997626	−	0.0688610i	$-0.978064\pi$
$757$	−25.5537	+	25.5537i	−0.928765	+	0.928765i	0.0688610	+	0.997626i	$0.478064\pi$
$758$		0			0
$759$	11.9804	+	8.70429i	0.434862	+	0.315946i
$760$		0			0
$761$	33.5597	−	24.3825i	1.21654	−	0.883867i	0.220730	−	0.975335i	$-0.429156\pi$
$761$	33.5597	−	24.3825i	1.21654	−	0.883867i	0.995808	+	0.0914685i	$0.0291561\pi$
$762$		0			0
$763$	−19.9592	+	3.16122i	−0.722571	+	0.114444i
$764$		0			0
$765$	15.3087	+	16.9540i	0.553487	+	0.612973i
$766$		0			0
$767$	−0.174306	+	0.342094i	−0.00629382	+	0.0123523i
$768$		0			0
$769$	−12.5753	+	4.08596i	−0.453476	+	0.147343i	−0.526845	−	0.849961i	$-0.676625\pi$
$769$	−12.5753	+	4.08596i	−0.453476	+	0.147343i	0.0733684	+	0.997305i	$0.476625\pi$
$770$		0			0
$771$	−18.2029	−	5.91447i	−0.655560	−	0.213004i
$772$		0			0
$773$	35.2872	+	5.58894i	1.26919	+	0.201020i	0.754468	−	0.656337i	$-0.227895\pi$
$773$	35.2872	+	5.58894i	1.26919	+	0.201020i	0.514723	+	0.857357i	$0.327895\pi$
$774$		0			0
$775$	−35.0832	+	39.1851i	−1.26023	+	1.40757i
$776$		0			0
$777$	−1.08404	+	6.84438i	−0.0388898	+	0.245541i
$778$		0			0
$779$	−9.11866	+	28.0643i	−0.326710	+	1.00551i
$780$		0			0
$781$	0.791796	+	2.43690i	0.0283327	+	0.0871990i
$782$		0			0
$783$	6.27076	+	3.19511i	0.224099	+	0.114184i
$784$		0			0
$785$	−14.7721	−	8.50098i	−0.527238	−	0.303413i
$786$		0			0
$787$	5.52431	+	34.8791i	0.196921	+	1.24331i	0.865972	+	0.500092i	$0.166700\pi$
$787$	5.52431	+	34.8791i	0.196921	+	1.24331i	−0.669052	+	0.743216i	$0.733300\pi$
$788$		0			0
$789$	−10.9823	−	15.1158i	−0.390980	−	0.538138i
$790$		0			0
$791$	−11.0562	+	15.2175i	−0.393112	+	0.541072i
$792$		0			0
$793$	−23.7820	−	23.7820i	−0.844524	−	0.844524i
$794$		0			0
$795$	−3.37264	+	8.82311i	−0.119615	+	0.312923i
$796$		0			0
$797$	3.73955	+	7.33928i	0.132462	+	0.259971i	0.947705	−	0.319148i	$-0.103397\pi$
$797$	3.73955	+	7.33928i	0.132462	+	0.259971i	−0.815243	+	0.579119i	$0.803397\pi$
$798$		0			0
$799$	3.32600			0.117666
$800$		0			0
$801$	35.5033			1.25445
$802$		0			0
$803$	−30.2130	−	59.2964i	−1.06619	−	2.09253i
$804$		0			0
$805$	18.8551	+	15.2247i	0.664555	+	0.536600i
$806$		0			0
$807$	8.38490	+	8.38490i	0.295162	+	0.295162i
$808$		0			0
$809$	27.9073	−	38.4111i	0.981168	−	1.35046i	0.0449695	−	0.998988i	$-0.485681\pi$
$809$	27.9073	−	38.4111i	0.981168	−	1.35046i	0.936198	−	0.351473i	$-0.114319\pi$
$810$		0			0
$811$	−23.5003	−	32.3454i	−0.825208	−	1.13580i	−0.988796	−	0.149273i	$-0.952307\pi$
$811$	−23.5003	−	32.3454i	−0.825208	−	1.13580i	0.163588	−	0.986529i	$-0.447693\pi$
$812$		0			0
$813$	−0.443532	−	2.80035i	−0.0155553	−	0.0982126i
$814$		0			0
$815$	20.4077	+	45.6634i	0.714850	+	1.59952i
$816$		0			0
$817$	−7.52102	−	3.83215i	−0.263127	−	0.134070i
$818$		0			0
$819$	−5.20075	−	16.0063i	−0.181729	−	0.559304i
$820$		0			0
$821$	−3.52278	+	10.8420i	−0.122946	+	0.378388i	−0.993521	−	0.113647i	$-0.963747\pi$
$821$	−3.52278	+	10.8420i	−0.122946	+	0.378388i	0.870575	+	0.492035i	$0.163747\pi$
$822$		0			0
$823$	3.45526	−	21.8156i	0.120443	−	0.760446i	−0.851348	−	0.524601i	$-0.824214\pi$
$823$	3.45526	−	21.8156i	0.120443	−	0.760446i	0.971791	−	0.235844i	$-0.0757856\pi$
$824$		0			0
$825$	0.970164	+	17.5658i	0.0337768	+	0.611564i
$826$		0			0
$827$	−38.4843	−	6.09531i	−1.33823	−	0.211955i	−0.554047	−	0.832485i	$-0.686917\pi$
$827$	−38.4843	−	6.09531i	−1.33823	−	0.211955i	−0.784182	+	0.620531i	$0.786917\pi$
$828$		0			0
$829$	36.3940	+	11.8251i	1.26402	+	0.410704i	0.862924	−	0.505334i	$-0.168631\pi$
$829$	36.3940	+	11.8251i	1.26402	+	0.410704i	0.401092	+	0.916038i	$0.368631\pi$
$830$		0			0
$831$	9.16491	−	2.97786i	0.317927	−	0.103301i
$832$		0			0
$833$	−0.728775	+	1.43030i	−0.0252506	+	0.0495570i
$834$		0			0
$835$	−24.3051	−	5.13047i	−0.841112	−	0.177547i
$836$		0			0
$837$	44.8757	−	7.10762i	1.55113	−	0.245675i
$838$		0			0
$839$	−29.4360	+	21.3865i	−1.01624	+	0.738344i	−0.965509	−	0.260368i	$-0.916156\pi$
$839$	−29.4360	+	21.3865i	−1.01624	+	0.738344i	−0.0507337	+	0.998712i	$0.516156\pi$
$840$		0			0
$841$	−21.3136	−	15.4852i	−0.734952	−	0.533974i
$842$		0			0
$843$	14.9237	−	14.9237i	0.514001	−	0.514001i
$844$		0			0
$845$	−6.40700	−	9.83559i	−0.220408	−	0.338355i
$846$		0			0
$847$	−18.3016	+	9.32515i	−0.628851	+	0.320416i
$848$		0			0
$849$			10.0903i			0.346298i
$850$		0			0
$851$			14.0225i			0.480684i
$852$		0			0
$853$	−22.7774	+	11.6057i	−0.779884	+	0.397371i	−0.798147	−	0.602462i	$-0.794186\pi$
$853$	−22.7774	+	11.6057i	−0.779884	+	0.397371i	0.0182632	+	0.999833i	$0.494186\pi$
$854$		0			0
$855$	−0.791326	+	15.5171i	−0.0270628	+	0.530675i
$856$		0			0
$857$	0.101626	−	0.101626i	0.00347146	−	0.00347146i	−0.705369	−	0.708840i	$-0.749219\pi$
$857$	0.101626	−	0.101626i	0.00347146	−	0.00347146i	0.708840	+	0.705369i	$0.249219\pi$
$858$		0			0
$859$	−8.75247	−	6.35904i	−0.298630	−	0.216968i	0.428372	−	0.903602i	$-0.359087\pi$
$859$	−8.75247	−	6.35904i	−0.298630	−	0.216968i	−0.727003	+	0.686635i	$0.759087\pi$
$860$		0			0
$861$	16.7759	−	12.1884i	0.571723	−	0.415381i
$862$		0			0
$863$	−30.0412	+	4.75806i	−1.02261	+	0.161966i	−0.645149	−	0.764057i	$-0.723205\pi$
$863$	−30.0412	+	4.75806i	−1.02261	+	0.161966i	−0.377466	+	0.926023i	$0.623205\pi$
$864$		0			0
$865$	−3.74514	−	35.1567i	−0.127339	−	1.19536i
$866$		0			0
$867$	−0.709697	+	1.39286i	−0.0241026	+	0.0473040i
$868$		0			0
$869$	44.4254	−	14.4347i	1.50703	−	0.489663i
$870$		0			0
$871$	−15.4358	−	5.01540i	−0.523022	−	0.169940i
$872$		0			0
$873$	−26.5396	−	4.20346i	−0.898230	−	0.142266i
$874$		0			0
$875$	0.121532	+	28.7901i	0.00410853	+	0.973285i
$876$		0			0
$877$	2.74744	−	17.3467i	0.0927746	−	0.585756i	−0.896879	−	0.442277i	$-0.854171\pi$
$877$	2.74744	−	17.3467i	0.0927746	−	0.585756i	0.989653	−	0.143479i	$-0.0458290\pi$
$878$		0			0
$879$	1.81850	−	5.59677i	0.0613365	−	0.188774i
$880$		0			0
$881$	9.30614	+	28.6414i	0.313532	+	0.964952i	0.976355	+	0.216175i	$0.0693583\pi$
$881$	9.30614	+	28.6414i	0.313532	+	0.964952i	−0.662823	+	0.748776i	$0.730642\pi$
$882$		0			0
$883$	−7.71075	−	3.92883i	−0.259488	−	0.132215i	0.319408	−	0.947617i	$-0.396516\pi$
$883$	−7.71075	−	3.92883i	−0.259488	−	0.132215i	−0.578895	+	0.815402i	$0.696516\pi$
$884$		0			0
$885$	−0.247678	+	0.0263844i	−0.00832561	+	0.000886903i
$886$		0			0
$887$	−1.11688	−	7.05168i	−0.0375010	−	0.236772i	0.961817	−	0.273693i	$-0.0882452\pi$
$887$	−1.11688	−	7.05168i	−0.0375010	−	0.236772i	−0.999318	+	0.0369206i	$0.988245\pi$
$888$		0			0
$889$	−7.43206	−	10.2294i	−0.249263	−	0.343081i
$890$		0			0
$891$	−9.10046	+	12.5257i	−0.304877	+	0.419627i
$892$		0			0
$893$	1.59968	+	1.59968i	0.0535313	+	0.0535313i
$894$		0			0
$895$	34.7842	+	1.77389i	1.16271	+	0.0592945i
$896$		0			0
$897$	4.29652	+	8.43239i	0.143456	+	0.281549i
$898$		0			0
$899$	17.1399			0.571647
$900$		0			0
$901$	22.7581			0.758183
$902$		0			0
$903$	2.69292	+	5.28516i	0.0896148	+	0.175879i
$904$		0			0
$905$	−5.95812	+	3.88118i	−0.198055	+	0.129015i
$906$		0			0
$907$	−26.0275	−	26.0275i	−0.864228	−	0.864228i	0.127598	−	0.991826i	$-0.459273\pi$
$907$	−26.0275	−	26.0275i	−0.864228	−	0.864228i	−0.991826	+	0.127598i	$0.959273\pi$
$908$		0			0
$909$	−19.9057	+	27.3979i	−0.660232	+	0.908731i
$910$		0			0
$911$	−18.2290	−	25.0901i	−0.603954	−	0.831271i	0.392109	−	0.919919i	$-0.371746\pi$
$911$	−18.2290	−	25.0901i	−0.603954	−	0.831271i	−0.996063	+	0.0886475i	$0.971746\pi$
$912$		0			0
$913$	−0.0369741	−	0.233445i	−0.00122366	−	0.00772591i
$914$		0			0
$915$	4.50641	−	21.3486i	0.148977	−	0.705764i
$916$		0			0
$917$	−6.23964	−	3.17925i	−0.206051	−	0.104988i
$918$		0			0
$919$	15.3051	+	47.1042i	0.504868	+	1.55383i	0.800992	+	0.598675i	$0.204306\pi$
$919$	15.3051	+	47.1042i	0.504868	+	1.55383i	−0.296123	+	0.955150i	$0.595694\pi$
$920$		0			0
$921$	−3.23530	+	9.95724i	−0.106607	+	0.328102i
$922$		0			0
$923$	−0.256164	+	1.61736i	−0.00843174	+	0.0532359i
$924$		0			0
$925$	−12.9166	+	10.5200i	−0.424697	+	0.345896i
$926$		0			0
$927$	42.7517	+	6.77120i	1.40415	+	0.222395i
$928$		0			0
$929$	−26.4817	−	8.60443i	−0.868837	−	0.282302i	−0.159522	−	0.987194i	$-0.550995\pi$
$929$	−26.4817	−	8.60443i	−0.868837	−	0.282302i	−0.709315	+	0.704892i	$0.750995\pi$
$930$		0			0
$931$	−1.03844	+	0.337408i	−0.0340333	+	0.0110581i
$932$		0			0
$933$	−3.63485	+	7.13380i	−0.119000	+	0.233550i
$934$		0			0
$935$	38.6980	−	17.2948i	1.26556	−	0.565599i
$936$		0			0
$937$	−30.3876	+	4.81293i	−0.992720	+	0.157231i	−0.631606	−	0.775290i	$-0.717604\pi$
$937$	−30.3876	+	4.81293i	−0.992720	+	0.157231i	−0.361115	+	0.932521i	$0.617604\pi$
$938$		0			0
$939$	−5.73702	+	4.16819i	−0.187221	+	0.136024i
$940$		0			0
$941$	−20.7455	−	15.0725i	−0.676284	−	0.491349i	0.195839	−	0.980636i	$-0.437257\pi$
$941$	−20.7455	−	15.0725i	−0.676284	−	0.491349i	−0.872123	+	0.489287i	$0.837257\pi$
$942$		0			0
$943$	29.6705	−	29.6705i	0.966203	−	0.966203i
$944$		0			0
$945$	15.6245	−	19.3502i	0.508264	−	0.629463i
$946$		0			0
$947$	5.43776	−	2.77067i	0.176703	−	0.0900348i	−0.363401	−	0.931633i	$-0.618385\pi$
$947$	5.43776	−	2.77067i	0.176703	−	0.0900348i	0.540105	+	0.841598i	$0.318385\pi$
$948$		0			0
$949$		−	42.5307i		−	1.38060i
$950$		0			0
$951$			5.94609i			0.192815i
$952$		0			0
$953$	−31.2327	+	15.9139i	−1.01173	+	0.515501i	−0.879591	−	0.475731i	$-0.842184\pi$
$953$	−31.2327	+	15.9139i	−1.01173	+	0.515501i	−0.132137	+	0.991232i	$0.542184\pi$
$954$		0			0
$955$	−51.2277	−	19.5818i	−1.65769	−	0.633652i
$956$		0			0
$957$	4.05390	−	4.05390i	0.131044	−	0.131044i
$958$		0			0
$959$	21.2860	+	15.4652i	0.687360	+	0.499396i
$960$		0			0
$961$	64.4400	−	46.8184i	2.07871	−	1.51027i
$962$		0			0
$963$	16.1102	−	2.55161i	0.519145	−	0.0822245i
$964$		0			0
$965$	−1.76227	+	3.06228i	−0.0567294	+	0.0985784i
$966$		0			0
$967$	23.9185	−	46.9427i	0.769167	−	1.50958i	−0.0889017	−	0.996040i	$-0.528336\pi$
$967$	23.9185	−	46.9427i	0.769167	−	1.50958i	0.858069	−	0.513535i	$-0.171664\pi$
$968$		0			0
$969$	−9.89370	+	3.21466i	−0.317831	+	0.103270i
$970$		0			0
$971$	45.8073	+	14.8837i	1.47003	+	0.477640i	0.931116	−	0.364723i	$-0.118836\pi$
$971$	45.8073	+	14.8837i	1.47003	+	0.477640i	0.538910	+	0.842363i	$0.318836\pi$
$972$		0			0
$973$	−58.7194	−	9.30024i	−1.88246	−	0.298152i
$974$		0			0
$975$	−4.54405	+	10.2839i	−0.145526	+	0.329348i
$976$		0			0
$977$	−7.09392	+	44.7893i	−0.226955	+	1.43294i	0.566377	+	0.824146i	$0.308344\pi$
$977$	−7.09392	+	44.7893i	−0.226955	+	1.43294i	−0.793332	+	0.608789i	$0.791656\pi$
$978$		0			0
$979$	20.3579	−	62.6552i	0.650641	−	2.00247i
$980$		0			0
$981$	5.69298	+	17.5212i	0.181763	+	0.559408i
$982$		0			0
$983$	−23.3773	−	11.9113i	−0.745619	−	0.379912i	0.0395305	−	0.999218i	$-0.487414\pi$
$983$	−23.3773	−	11.9113i	−0.745619	−	0.379912i	−0.785149	+	0.619307i	$0.787414\pi$
$984$		0			0
$985$	10.2437	−	9.24956i	0.326390	−	0.294716i
$986$		0			0
$987$	−0.248692	−	1.57018i	−0.00791595	−	0.0499794i
$988$		0			0
$989$	7.05514	+	9.71057i	0.224340	+	0.308778i
$990$		0			0
$991$	−23.5809	+	32.4563i	−0.749072	+	1.03101i	0.248973	+	0.968510i	$0.419907\pi$
$991$	−23.5809	+	32.4563i	−0.749072	+	1.03101i	−0.998045	+	0.0624985i	$0.980093\pi$
$992$		0			0
$993$	−15.0516	−	15.0516i	−0.477647	−	0.477647i
$994$		0			0
$995$	6.37023	+	23.6409i	0.201950	+	0.749467i
$996$		0			0
$997$	13.4228	+	26.3437i	0.425105	+	0.834315i	0.999872	+	0.0159979i	$0.00509251\pi$
$997$	13.4228	+	26.3437i	0.425105	+	0.834315i	−0.574767	+	0.818317i	$0.694907\pi$
$998$		0			0
$999$	14.3907			0.455301

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	800.2.bq.c.223.5	✓	64
4.3	odd	2		800.2.bq.d.223.4	yes	64
25.12	odd	20		800.2.bq.d.287.4	yes	64
100.87	even	20	inner	800.2.bq.c.287.5	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
800.2.bq.c.223.5	✓	64	1.1	even	1	trivial
800.2.bq.c.287.5	yes	64	100.87	even	20	inner
800.2.bq.d.223.4	yes	64	4.3	odd	2
800.2.bq.d.287.4	yes	64	25.12	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 800 = 2^{5} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	800.bq (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.366689 + 0.719668i) q^{3} +(-0.581776 - 2.15906i) q^{5} +(1.82087 + 1.82087i) q^{7} +(1.37989 - 1.89926i) q^{9} +(-2.56052 - 3.52425i) q^{11} +(-0.435508 - 2.74969i) q^{13} +(1.34048 - 1.21039i) q^{15} +(-3.87720 - 1.97553i) q^{17} +(-0.914631 - 2.81494i) q^{19} +(-0.642727 + 1.97811i) q^{21} +(-0.658396 + 4.15695i) q^{23} +(-4.32307 + 2.51218i) q^{25} +(4.26611 + 0.675685i) q^{27} +(1.54965 + 0.503512i) q^{29} +(10.0043 - 3.25059i) q^{31} +(1.59738 - 3.13503i) q^{33} +(2.87202 - 4.99069i) q^{35} +(3.29071 - 0.521197i) q^{37} +(1.81917 - 1.32170i) q^{39} +(-8.06571 - 5.86008i) q^{41} +(2.01659 - 2.01659i) q^{43} +(-4.90341 - 1.87433i) q^{45} +(-0.681030 + 0.347002i) q^{47} -0.368901i q^{49} -3.51471i q^{51} +(-4.65994 + 2.37436i) q^{53} +(-6.11942 + 7.57863i) q^{55} +(1.69044 - 1.69044i) q^{57} +(-0.111573 - 0.0810625i) q^{59} +(9.77366 - 7.10098i) q^{61} +(5.97090 - 0.945698i) q^{63} +(-5.68337 + 2.53999i) q^{65} +(2.64671 - 5.19446i) q^{67} +(-3.23305 + 1.05048i) q^{69} +(-0.559408 - 0.181763i) q^{71} +(15.0889 + 2.38985i) q^{73} +(-3.39316 - 2.18999i) q^{75} +(1.75483 - 11.0795i) q^{77} +(-3.31359 + 10.1982i) q^{79} +(-1.09829 - 3.38020i) q^{81} +(0.0483434 + 0.0246322i) q^{83} +(-2.00963 + 9.52042i) q^{85} +(0.205879 + 1.29987i) q^{87} +(8.88915 + 12.2349i) q^{89} +(4.21381 - 5.79981i) q^{91} +(6.00781 + 6.00781i) q^{93} +(-5.54552 + 3.61241i) q^{95} +(-5.19630 - 10.1983i) q^{97} -10.2267 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 2 q^{5} - 4 q^{7} + 4 q^{13} - 22 q^{15} + 8 q^{17} + 18 q^{19} - 16 q^{21} - 8 q^{23} + 40 q^{25} - 18 q^{27} + 20 q^{31} + 44 q^{33} - 38 q^{35} - 10 q^{37} + 36 q^{39} - 16 q^{41} - 32 q^{43}+ \cdots - 132 q^{99}+O(q^{100}) \) 64 * q + 2 * q^5 - 4 * q^7 + 4 * q^13 - 22 * q^15 + 8 * q^17 + 18 * q^19 - 16 * q^21 - 8 * q^23 + 40 * q^25 - 18 * q^27 + 20 * q^31 + 44 * q^33 - 38 * q^35 - 10 * q^37 + 36 * q^39 - 16 * q^41 - 32 * q^43 + 14 * q^45 - 8 * q^47 - 22 * q^53 + 24 * q^55 - 8 * q^57 + 4 * q^59 - 36 * q^61 - 18 * q^63 - 24 * q^65 + 26 * q^67 + 60 * q^69 - 70 * q^71 - 12 * q^73 - 66 * q^75 + 48 * q^77 - 16 * q^79 - 24 * q^81 + 52 * q^83 - 46 * q^85 + 144 * q^87 - 60 * q^89 + 30 * q^91 + 20 * q^93 + 8 * q^95 - 56 * q^97 - 132 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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